Global attractor for weakly damped nonlinear Schrödinger equations in L2(R)L2(R)

We prove that the weakly damped nonlinear Schrödinger flow in L2(R)L2(R) provides a dynamical system which possesses a global attractor. The proof relies on the continuity of the Schrödinger flow for the weak topology in L2(R)L2(R).